Let the linear transformation T : R² → R² be such that T(1, 1) = (1, –2), T(-1,1) = (-4, 1) Find a formula for Т(а, у)аnd use that formula to get T(5, —3) tip : write an arbitrary vector (x, y) as a linear , combinationo f (1, 1) and (-1, 1))

The cross product of two vectors in R' is defined by 日-屏 [b1 azb3 – azb2 ai a2 b2 azbı – aıb3 b3 aıb2 – azbı аз Let i . Find the matrix A of the linear transformation from R to R° given by T(7) = j x a. A = || ||

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2. Let T : R² → R² be a linear transformation such that: 1 -2 (i) T maps vector u = into the vector a = [ 5 3 (ii) T maps vector v = [³] into the vector b = [ Use the fact that T is a linear transformation to find T(3u +2v). -4